Deformation of thin flexible elastic wire in pure bending & twisting

A constant section long slender wire made of linear elastic high
elongation material like fiberglass has ( flexural, torsional )
properties/rigidities ( EI, GJ ).It develops (flexural,torsional)
curvatures (m, t) = ( M/EI, T/GJ ) on application of moments ( M,T )
as per ( Euler-Bernoulli, St.Venant?) Laws.
Is it correct to say that this wire deforms to a helix of
(x, y, z) = ( m cos(th), m sin(th), t * th ) / (m^2 + t^2) ?
If correct, has it been verified as a standard geometric non-linear
problem by FEM?
Best Regards,
( could not X post the same post yesterday along with sci.math )
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